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If it’s not algebricaly proven don’t call it an ‘identity’... even if a calculator were to confirm it to some arbitrary number of digits, that’d just be a more-
by qubex 6y ago
If it’s not algebricaly proven don’t call it an ‘identity’... even if a calculator were to confirm it to some arbitrary number of digits, that’d just be a more-or-less accurate approximation. ‘Identity’ denotes a far more profound relationship and the term should be reserved for use in such cases.
- peter_d_sherman 6y agoThat's what I'm trying to ascertain... is this an identity or not? (Note, I changed my comment to 'potential identity' rather than 'identity'). That, and are there any simple(r) identities for phi in terms of e, and e in terms of phi...?
- deleted 6y ago[deleted]
- qubex 6y agoAs somebody in that thread points out, using division you can trivially construct an identity by taking the definition of φ and replacing any integer with expressions such as π÷π for 1 and (e+e+e+e+e)/e for 5.